The terminology for categorizing triangles is more than two thousand years old, having been defined on the very first page of Euclid's Elements.

Types of triangle Euler diagram of types of triangles, using the definition that isosceles triangles have at least 2 equal sides (i.e., equilateral triangles are isosceles). This article is about triangles in Euclidean geometry, and in particular, the Euclidean plane, except where otherwise noted. If the entire geometry is only the Euclidean plane, there is only one plane and all triangles are contained in it however, in higher-dimensional Euclidean spaces, this is no longer true.

In other words, there is only one plane that contains that triangle, and every triangle is contained in some plane. In Euclidean geometry, any three points, when non- collinear, determine a unique triangle and simultaneously, a unique plane (i.e. A triangle with vertices A, B, and C is denoted △ A B C riangle ABC. It is one of the basic shapes in geometry. A triangle is a polygon with three edges and three vertices.

Isosceles triangle definition geometry